"click on a notification I get and "/admin/" string added in my url"
This is because you use qa_path(). Problem is: The AJAX call goes to the server, the server does not know that you are at /admin/ and assumes you are in the root. It returns the relative path "./123/question" which gets added to your *recent* URL. That's why you must use an absolute path, not relative ones. I hope this explanation makes it clear ;-)
The "https" issue is indeed a special one, and maybe you are the only one having this issue currently. My ideas:
1. Do the ajax call with https? see "var eventNotify = ..." (use the https instead http)
2. Do not use https anyways.
3. Maybe there is a way for the server to check if it is a httpS request, then you could build a workaround.
The error message you mentioned in your question, is it coming from JS or PHP? I assume JS, then see here as well: http://stackoverflow.com/q/22196927/1066234